Black-Scholes Formula for Valuing European Options
P = current asset price.
r% = risk-free rate (continuous, per time unit).
s% = volatility (continuous, per time unit).
T = term of option (same time unit as r% and s%).
X = exercise price of option.
N(z) = probability that a unit normal random variable is less than z.
Call Value = P × N(d
Put Value = Call Value + Q – P
= LN(P/Q)/v + v/2, d
Q = Xe
= asset's useful life expectancy.
= starting book value.
= salvage value.
= declining-balance factor expressed as a percentage.
= period number.
= depreciation expense during period j.
= remaining depreciable value at end of period j
= remaining book value = RBV
= number of months in partial first year.
) – Q × N(d
( – T × r % / 1 0 0 )
Appendix E: Formulas Used
= SBV – SAL